Bálint Varga

Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.

Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google’s PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections in the brain graph. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges.

Parameterizable consensus connectomes from the Human Connectome Project: the Budapest Reference Connectome Server v3.0

Connections of the living human brain, on a macroscopic scale, can be mapped by a diffusion MR imaging based workflow. Since the same anatomic regions can be corresponded between distinct brains, one can compare the presence or the absence of the edges, connecting the very same two anatomic regions, among multiple cortices. Previously, we have constructed the consensus braingraphs on 1015 vertices first in five, then in 96 subjects in the Budapest Reference Connectome Server v1.0 and v2.0, respectively. Here we report the construction of the version 3.0 of the server, generating the common edges of the connectomes of variously parameterizable subsets of the 1015-vertex connectomes of 477 subjects of the Human Connectome Project’s 500-subject release. The consensus connectomes are downloadable in CSV and GraphML formats, and they are also visualized on the server’s page. The consensus connectomes of the server can be considered as the “average, healthy” human connectome since all of their connections are present in at least k subjects, where the default value of

Brain size bias compensated graph-theoretical parameters are also better in women’s structural connectomes

k=209

The braingraph.org database of high resolution structural connectomes and the brain graph tools

k=209, but it can also be modified freely at the web server. The webserver is available at http://connectome.pitgroup.org.

The Robustness and the Doubly-Preferential Attachment Simulation of the Consensus Connectome Dynamics of the Human Brain

The human braingraph or the connectome is the object of an intensive research today. The advantage of the graph-approach to brain science is that the rich structures, algorithms and definitions of graph theory can be applied to the anatomical networks of the connections of the human brain. In these graphs, the vertices correspond to the small (1–1.5 cm2) areas of the gray matter, and two vertices are connected by an edge, if a diffusion-MRI based workflow finds fibers of axons, running between those small gray matter areas in the white matter of the brain. One main question of the field today is discovering the directions of the connections between the small gray matter areas. In a previous work we have reported the construction of the Budapest Reference Connectome Server http://connectome.pitgroup.org from the data recorded in the Human Connectome Project of the NIH. The server generates the consensus braingraph of 96 subjects in Version 2, and of 418 subjects in Version 3, according to selectable parameters. After the Budapest Reference Connectome Server had been published, we recognized a surprising and unforeseen property of the server. The server can generate the braingraph of connections that are present in at least k graphs out of the 418, for any value of k = 1, 2, …, 418. When the value of k is changed from k = 418 through 1 by moving a slider at the webserver from right to left, certainly more and more edges appear in the consensus graph. The astonishing observation is that the appearance of the new edges is not random: it is similar to a growing shrub. We refer to this phenomenon as the Consensus Connectome Dynamics. We hypothesize that this movement of the slider in the webserver may copy the development of the connections in the human brain in the following sense: the connections that are present in all subjects are the oldest ones, and those that are present only in a decreasing fraction of the subjects are gradually the newer connections in the individual brain development. An animation on the phenomenon is available at https://youtu.be/yxlyudPaVUE. Based on this observation and the related hypothesis, we can assign directions to some of the edges of the connectome as follows: Let Gk + 1 denote the consensus connectome where each edge is present in at least k+1 graphs, and let Gk denote the consensus connectome where each edge is present in at least k graphs. Suppose that vertex v is not connected to any other vertices in Gk+1, and becomes connected to a vertex u in Gk, where u was connected to other vertices already in Gk+1. Then we direct this (v, u) edge from v to u.

PDB_Amyloid: An Extended Live Amyloid Structure List from the PDB

In our previous study it was shown that the female connectomes have significantly better, deep graphtheoretical parameters, related to superior “connectivity”, than the connectome of the males. Since the average female brain is smaller than the average male brain, one cannot rule out that the significant advantages are due to the sizeand not to the sex-differences in the data. To filter out the possible brain-volume related artifacts, we have chosen 36 small male and 36 large female brains such that all the brains in the female set are larger than all the brains in the male set. For the sets, we have constructed the corresponding braingraphs and computed numerous graph-theoretical parameters. We have found that (i) the small male brains lack the better connectivity, shown in our previous study for female brains in general; (ii) in numerous parameters (more exactly, 13 parameters, listed in Table 2), the connectomes computed from the large-brain females, still have the (statistically uncorrected) significant, deep connectivity advantages, demonstrated in our previous study. Electronic supplementary material The online version of this article (doi:10.1007/s11682-017-9720-0) contains supplementary material, which is available to authorized users. Vince Grolmusz grolmusz@pitgroup.org Balázs Szalkai szalkai@pitgroup.org Bálint Varga balorkany@pitgroup.org 1 PIT Bioinformatics Group, Eötvös University, H-1117, Budapest, Hungary 2 Uratim Ltd., H-1118, Budapest, Hungary

Comparing advanced graph-theoretical parameters of the connectomes of the lobes of the human brain

Genome-wide association studies (GWAS) opened new horizons in genomics and medicine by discovering novel genetic factors in numerous health conditions. The analogous analysis of the correlations of large quantities of psychological and brain imaging measures may yield similarly striking results in the brain science. Smith et al. (Nat Neurosci. 18(11): 1565–1567, 2015) presented a study of the associations between MRI-detected resting-state functional connectomes and behavioral data, based on the Human Connectome Project’s (HCP) data release. Here we analyze the pairwise correlations between 717 psychological-, anatomical- and structural connectome–properties, based also on the Human Connectome Project’s 500-subject dataset. For the connectome properties, we have focused on the structural (or anatomical) connectomes, instead of the functional connectomes. For the structural connectome analysis we have computed and publicly deposited structural braingraphs at the site http://braingraph.org. Numerous non-trivial and hard-to-compute graph-theoretical parameters (like minimum bisection width, minimum vertex cover, eigenvalue gap, maximum matching number, maximum fractional matching number) were computed for braingraphs of each subject, gained from the left- and right hemispheres and the whole brain. The correlations of these parameters, as well as other anatomical and behavioral measures were detected and analyzed. For discovering and visualizing the most interesting correlations in the 717 x 717 matrix, we have applied the maximum spanning tree method. Apart from numerous natural correlations, which describe parameters computable or approximable from one another, we have found several significant, novel correlations in the dataset, e.g., between the score of the NIH Toolbox 9-hole Pegboard Dexterity Test and the maximum weight graph theoretical matching in the left hemisphere. We also have found correlations described very recently and independently from the HCP-dataset: e.g., between gambling behavior and the number of the connections leaving the insula: these already known findings independently validate the power of our method.

The Budapest Reference Connectome Server v2.0.

Based on the data of the NIH-funded Human Connectome Project, we have computed structural connectomes of 426 human subjects in five different resolutions of 83, 129, 234, 463 and 1015 nodes and several edge weights. The graphs are given in anatomically annotated GraphML format that facilitates better further processing and visualization. For 96 subjects, the anatomically classified sub-graphs can also be accessed, formed from the vertices corresponding to distinct lobes or even smaller regions of interests of the brain. For example, one can easily download and study the connectomes, restricted to the frontal lobes or just to the left precuneus of 96 subjects using the data. Partially directed connectomes of 423 subjects are also available for download. We also present a GitHub-deposited set of tools, called the Brain Graph Tools, for several processing tasks of the connectomes on the site http://braingraph.org.